Analysis of zz-www.sudokuwiki.org-0056-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=56

level: hard

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=56

position: 8.5.....6.1......2.26.1.5...6.4.1.....8...7.....5.8.6...2.4.13.5......8.9.....2.7 initial

Autosolve

position: 8.5....16.1......2.26.1.5...6.4.1....58.6.7.....5.8.6.6.2.4.13.5.....68.9.....2.7 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # D7: 9 => CTR => D7: 7,8
* DIS # F7: 7 => CTR => F7: 5,9
* CNT   2 HDP CHAINS /   4 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* DIS # D7: 9 => CTR => D7: 7,8
* STA D7: 7,8
* CNT   1 HDP CHAINS /   6 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Pair Reduction Position

position: 8.5....16.1......2.26.1.5...6.4.1....58.6.7.....5.8.6.6.2.4.13.5.....68.9.....2.7 pair_reduction
Pair Reduction

See section Pair Reduction for the HDP chains leading to this result.

Deep Pair Reduction

Deep Pair Reduction

Time used: 0:00:11.855977

The following important HDP chains were detected:

* DIS # D2: 7,8 # B1: 4,7 => CTR => B1: 3,9
* PRF # D2: 7,8 + B1: 3,9 => SOL
* STA D2: 7,8
* CNT   2 HDP CHAINS /   6 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Details

Positions

8.5.....6.1......2.26.1.5...6.4.1.....8...7.....5.8.6...2.4.13.5......8.9.....2.7 initial
8.5....16.1......2.26.1.5...6.4.1....58.6.7.....5.8.6.6.2.4.13.5.....68.9.....2.7 autosolve
8.5....16.1......2.26.1.5...6.4.1....58.6.7.....5.8.6.6.2.4.13.5.....68.9.....2.7 pair_reduction
895327416417856392326914578769431825158269743234578961682745139573192684941683257 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (6)
E2: 5,8
B7: 7,8
E9: 5,8
I7: 5,9
I8: 4,9
H9: 4,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A5,A6: 1.. / A5 = 1  => 14 pairs (_) / A6 = 1  => 17 pairs (_)
I5,I6: 1.. / I5 = 1  => 17 pairs (_) / I6 = 1  => 14 pairs (_)
C8,C9: 1.. / C8 = 1  =>  8 pairs (_) / C9 = 1  =>  6 pairs (_)
D8,D9: 1.. / D8 = 1  =>  6 pairs (_) / D9 = 1  =>  8 pairs (_)
A5,I5: 1.. / A5 = 1  => 14 pairs (_) / I5 = 1  => 17 pairs (_)
A6,I6: 1.. / A6 = 1  => 17 pairs (_) / I6 = 1  => 14 pairs (_)
C8,D8: 1.. / C8 = 1  =>  8 pairs (_) / D8 = 1  =>  6 pairs (_)
C9,D9: 1.. / C9 = 1  =>  6 pairs (_) / D9 = 1  =>  8 pairs (_)
H4,H5: 2.. / H4 = 2  =>  0 pairs (*) / H5 = 2  =>  0 pairs (X)
A6,E6: 2.. / A6 = 2  => 16 pairs (_) / E6 = 2  => 14 pairs (_)
I8,H9: 4.. / I8 = 4  => 12 pairs (_) / H9 = 4  =>  0 pairs (X)
E2,F2: 5.. / E2 = 5  =>  5 pairs (_) / F2 = 5  =>  0 pairs (X)
H4,I4: 5.. / H4 = 5  =>  0 pairs (X) / I4 = 5  => 12 pairs (_)
I7,H9: 5.. / I7 = 5  =>  0 pairs (X) / H9 = 5  => 12 pairs (_)
F7,I7: 5.. / F7 = 5  => 12 pairs (_) / I7 = 5  =>  0 pairs (X)
E2,E9: 5.. / E2 = 5  =>  5 pairs (_) / E9 = 5  =>  0 pairs (X)
H4,H9: 5.. / H4 = 5  =>  0 pairs (X) / H9 = 5  => 12 pairs (_)
I4,I7: 5.. / I4 = 5  => 12 pairs (_) / I7 = 5  =>  0 pairs (X)
D2,F2: 6.. / D2 = 6  =>  6 pairs (_) / F2 = 6  =>  6 pairs (_)
D9,F9: 6.. / D9 = 6  =>  6 pairs (_) / F9 = 6  =>  6 pairs (_)
D2,D9: 6.. / D2 = 6  =>  6 pairs (_) / D9 = 6  =>  6 pairs (_)
F2,F9: 6.. / F2 = 6  =>  6 pairs (_) / F9 = 6  =>  6 pairs (_)
H2,H3: 7.. / H2 = 7  =>  8 pairs (_) / H3 = 7  =>  9 pairs (_)
E4,E6: 7.. / E4 = 7  =>  8 pairs (_) / E6 = 7  => 16 pairs (_)
G2,I3: 8.. / G2 = 8  =>  0 pairs (X) / I3 = 8  => 10 pairs (_)
G4,I4: 8.. / G4 = 8  => 10 pairs (_) / I4 = 8  =>  0 pairs (X)
B7,B9: 8.. / B7 = 8  =>  7 pairs (_) / B9 = 8  =>  0 pairs (X)
D3,I3: 8.. / D3 = 8  =>  0 pairs (X) / I3 = 8  => 10 pairs (_)
B7,D7: 8.. / B7 = 8  =>  7 pairs (_) / D7 = 8  =>  0 pairs (X)
E2,E9: 8.. / E2 = 8  =>  0 pairs (X) / E9 = 8  =>  5 pairs (_)
G2,G4: 8.. / G2 = 8  =>  0 pairs (X) / G4 = 8  => 10 pairs (_)
I3,I4: 8.. / I3 = 8  => 10 pairs (_) / I4 = 8  =>  0 pairs (X)
B1,C2: 9.. / B1 = 9  =>  8 pairs (_) / C2 = 9  => 16 pairs (_)
I7,I8: 9.. / I7 = 9  => 12 pairs (_) / I8 = 9  =>  0 pairs (X)
B1,B6: 9.. / B1 = 9  =>  8 pairs (_) / B6 = 9  => 16 pairs (_)
* DURATION: 0:00:58.147961  START: 18:37:41.019863  END: 18:38:39.167824 2017-04-30
* CP COUNT: (35)
* SOLUTION FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:11.747147  START: 18:38:52.252031  END: 18:39:03.999178 2017-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0056-base-pr-002.dot
* REASONING
* DIS # D2: 7,8 # B1: 4,7 => CTR => B1: 3,9
* PRF # D2: 7,8 + B1: 3,9 => SOL
* STA D2: 7,8
* CNT   2 HDP CHAINS /   6 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=56

Solution

position: 895327416417856392326914578769431825158269743234578961682745139573192684941683257 solved
Solution

See section Deep Pair Reduction for the HDP chains leading to this result.

Appendix: Full HDP Chains

A1. Pair Reduction Analysis

Full list of HDP chains traversed:

* INC # D7: 7,8 => UNS
* DIS # D7: 9 => CTR => D7: 7,8
* INC # F7: 5,9 => UNS
* DIS # F7: 7 => CTR => F7: 5,9
* CNT   4 HDP CHAINS /   4 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # D7: 7,8 => UNS
* DIS # D7: 9 => CTR => D7: 7,8
* INC D7: 7,8 # D2: 7,8 => UNS
* INC D7: 7,8 # D3: 7,8 => UNS
* INC D7: 7,8 # F2: 5,9 => UNS
* INC D7: 7,8 # F2: 3,4,6,7 => UNS
* STA D7: 7,8
* CNT   6 HDP CHAINS /   6 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # D2: 7,8 => UNS
* INC # D3: 7,8 => UNS
* INC # F2: 5,9 => UNS
* INC # F2: 3,4,6,7 => UNS
* DIS # D2: 7,8 # B1: 4,7 => CTR => B1: 3,9
* PRF # D2: 7,8 + B1: 3,9 => SOL
* STA D2: 7,8
* CNT   6 HDP CHAINS /   6 HYP OPENED